Dynamical Behavior and Exact Traveling Wave Solutions for Three Special Variants of the Generalized Tzitzeica Equation

The dynamics and bifurcations of traveling wave solutions are studied for three nonlinear wave equations. A new phenomenon, such as a composed orbit, which consists of two or three heteroclinic orbits, may correspond to a solitary wave solution, a periodic wave solution or a peakon solution, is found for the equations. Some previous results are extended.     

Exact Loop Wave Solutions and Cusp Wave Solutions of the Fujimoto-Watanabe Equation

In this paper, the theory of dynamical systems is employed to investigate loop waves and cusp waves of the Fujimoto-Watanabe equation. These waves contain solitary loop waves, periodic loop waves, peakons and periodic cusp waves. Under fixed parameter conditions, their exact explicit parametric expressions are given.     

Exact plasma wave solutions for isothermal electron fluid plasma

Quasistationary electron plasma waves of arbitrary amplitude and speed that are exact solutions of the isothermal electron fluid equations are shown to exist.     

从题序看张先词的创新及对苏轼的影响

张先是第一个大量使用题序的词人,张先词的题序内容丰富多彩,记录士大夫交游唱和的题序使词带有了诗化的特点。散文化的题序使词带有叙事的色彩。张先与苏轼在熙宁年间交往甚密,资料表明两人有师法相传的关系,张先词在题序上的创新,对苏轼以诗为词产生了影响。     

从白驹场地域的历史归属看施耐庵里籍问题

正史、志乘、工具书载白驹场隶兴化,白驹场为《水浒》作者施耐庵故里,数典不能忘祖。     

南剑学风对杨时教育思想形成的影响

在"闽学鼻祖"杨时少年求学时期,形成于福建南剑州州治一带的南剑学风,既促进了当地的人才培养、学术思想体系形成及文脉传承,同时也对杨时教育思想的形成起到了重要的影响作用。     

Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential

We study analytically and numerically the stability of the standing waves for a nonlinear Schrödinger equation with a point defect and a power type nonlinearity. A major difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves. This is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing-wave solution is stable in and unstable in under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercritical nonlinear interaction, we prove the instability by blowup in the repulsive case by showing a virial theorem and using a minimization method involving two constraints. In the subcritical radial case, unstable bound states cannot collapse, but rather narrow down until they reach the stable regime (a finite-width instability). In the nonradial repulsive case, all bound states are unstable, and the instability is manifested by a lateral drift away from the defect, sometimes in combination with a finite-width instability or a blowup instability.     

Lattice point counts for the Shi arrangement and other affinographic hyperplane arrangements

Hyperplanes of the form xj=xi+c are called affinographic. For an affinographic hyperplane arrangement in Rn, such as the Shi arrangement, we study the function f(m) that counts integral points in n[1,m] that do not lie in any hyperplane of the arrangement. We show that f(m) is a piecewise polynomial function of positive integers m, composed of terms that appear gradually as m increases. Our approach is to convert the problem to one of counting integral proper colorations of a rooted integral gain graph.An application is to interval coloring in which the interval of available colors for vertex vi has the form [hi+1,m].A related problem takes colors modulo m; the number of proper modular colorations is a different piecewise polynomial that for large m becomes the characteristic polynomial of the arrangement (by which means Athanasiadis previously obtained that polynomial). We also study this function for all positive moduli.     

王曾与石介的交游

王曾是北宋名相,石介是北宋著名理学家,两人互相敬服对方的人格,彼此之间建立了相当亲密、融洽的私人关系。他们的交往对当时朝廷的政治文化产生了较大的影响。政治方面,他们都把国家安危放在首位,能够冒死上谏,有效阻止统治者的错误做法,安定人心;文化方面,两人均关注教育,兴办儒学并促进朝廷对地方教育的重视,改变了所辖地区颓废奢靡之风。两人的交往体现了他们忠心为国的高尚情操,充分展现了两位当世名臣的风范。